Relative energy approach to a diffuse interface model of a compressible two-phase flow

0503415 - MÚ 2020 RIV GB eng J - Článek v odborném periodiku
Feireisl, Eduard - Petcu, M. - Pražák, D.
Relative energy approach to a diffuse interface model of a compressible two-phase flow.
Mathematical Methods in the Applied Sciences. Roč. 42, č. 5 (2019), s. 1465-1479. ISSN 0170-4214. E-ISSN 1099-1476
Grant CEP: GA MŠMT(CZ) 7AMB17FR053
Institucionální podpora: RVO:67985840
Klíčová slova: Allen-Cahn equation * compressible Navier-Stokes system * two-phase flow
Obor OECD: Pure mathematics
Impakt faktor: 1.626, rok: 2019
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1002/mma.5436

We propose a simple model for a two-phase flow with a diffuse interface. The model couples the compressible Navier-Stokes system governing the evolution of the fluid density and the velocity field with the Allen-Cahn equation for the order parameter. We show that the model is thermodynamically consistent, in particular, a variant of the relative energy inequality holds. As a corollary, we show the weak-strong uniqueness principle, meaning any weak solution coincides with the strong solution emanating from the same initial data on the life span of the latter. Such a result plays a crucial role in the analysis of the associated numerical schemes. Finally, we perform the low Mach number limit obtaining the standard incompressible model.
Trvalý link: http://hdl.handle.net/11104/0295227